The wavelengths of the dark lines are exactly the same as those of bright lines in the absorption spectrum.

Did you perhaps read that as meaning:
"The wavelengths of the dark lines in the absorption spectrum are exactly the same as those of bright lines in the corresponding emmission spectrum."

But it does not actually say that - the grammar of the original question related bright lines to the absorption spectrum.
If that is the only information - then your reading was in error.

You want me to say you were right and your teacher wrong? - I don't have enough information.
I think your answer is better as a long answer, because it needs the explanation, and hers best for true-false.
Exam questions at this level are best considered in the context of the course and the teacher - which is why I asked about what your teacher would normally be referring to.